Kac-Moody algebras is one of the advanced fields of Mathematical research, which is developing rapidly in recent years due to its interesting connections and applications to many areas in Mathematics and Mathematical Physics like Quantum Physics, Number theory, Combinatorics, Non-linear differential equations etc. A specific class of indefinite non-hyperbolic Kac-Moody Algebras EHG2 was considered by Uma Maheswari  wherein a realization for these algebras as a graded Lie algebra of Kac-Moody type was obtained. The homology modules and the structure of the components of the maximal ideal upto level three were computed. In this paper, a specific class of the family QHG2 is considered. Using this realization as a graded Lie algebra of Kac-Moody type, the homology modules upto level five are computed. The structure of the components of the maximal ideal upto level four is determined. To compute these we combine the theory of homological techniques and spectral sequences theory.